Learning stabilizable symplectic ODE-net-based MPC for autonomous vehicle trajectory tracking

Neural network (NN)-based Model predictive control (MPC) can model vehicle dynamics with uncertainty and provide higher tracking accuracy for autonomous vehicle trajectory tracking tasks. However, the existing NN-based MPCs employ fully connected layers with non-interpretable structures, leading to suboptimal modeling accuracy. Additionally, these methods often incur a high computational burden, and theoretical properties such as feasibility and stability are lost. To address these issues, we propose a deep stabilizing Symplectic ODE-Net (SymODEN)-based MPC approach for trajectory tracking. Firstly, the SymODEN is applied to learn the vehicle lateral dynamics and a SymODEN-based MPC is established, which achieves higher tracking accuracy. Then a deep stabilizing controller for MPC is proposed. By incorporating constraints into the control network and including the error bound between the learning system and the true system in the loss function, we conduct a stability analysis and identify the subset of the region of attraction. This subset is proven to be a subset of the feasible region of the learning MPC. Finally, the CarSim-Matlab co-simulations verify that our method significantly improves tracking performance compared to the existing works. Tracking error and computational time are reduced by at most 99.7% and 99.8% respectively in different manoeuvres.